An Improved Locally Linear Embedding Algorithm by Using Recurrent Neural Networks
The well known LLE, i.e., Locally Linear Embedding, is a famous manifold learning algorithm. It has been extensively applied in many real-world problems in recent years. Successful applications of LLE rely on the associated adjacency graph, which is generally constructed by k-nearest
neighbor (k-NN) method. Since the k-NN method requires a fixed size of the neighborhood for each data point on the manifolds, it may result in a bad adjacency graph, especially in the case that multiple manifolds intersect each other. This paper proposes an improved locally linear
embedding algorithm, called iLLE. To construct the proper adjacency graph, the iLLE combines the sparsity property of k-norm with convex hull constraint. It can be formed as an optimization program and a model of recurrent neural networks is designed to solve it. Rigorous mathematical
analysis is provided to show that the network model can efficiently solve this optimization program, and a suitable adjacency graph can be constructed thereafter. Unlike the original LLE, the iLLE can not only select the neighborhood for each point adaptively, but also find the nonlinear intrinsic
structures among multiple manifolds. Experiments demonstrate that the iLLE achieves significant improvements over the original LLE. It also gives a good example of applying recurrent neural networks to manifold learning problems.
Keywords: Locally Linear Embedding; Manifold Learning; Neighborhood Selection; Recurrent Neural Networks; Sparse Representation
Document Type: Research Article
Affiliations: School of Computer and Information Science, Southwest University, Chongqing, 400715, China
Publication date: 01 January 2016
- Journal of Computational and Theoretical Nanoscience is an international peer-reviewed journal with a wide-ranging coverage, consolidates research activities in all aspects of computational and theoretical nanoscience into a single reference source. This journal offers scientists and engineers peer-reviewed research papers in all aspects of computational and theoretical nanoscience and nanotechnology in chemistry, physics, materials science, engineering and biology to publish original full papers and timely state-of-the-art reviews and short communications encompassing the fundamental and applied research.
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